Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #20338 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33329 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | C22×C42 |
| commutator | C4 | C22×C42×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| socle | C2×C13 | C22×#97 |
| prime radical | C2×C13×#41 | C2×C4 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ G | |
716 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,22,18,24,29,37,19,23,28,38,30,20,31,33)(16,21,26,35,27,36,41,45,25,34,39,44,40,32,42,43);(15,20,23,24)(17,28)(21,32,34,36)(22,37,38,33)(26,39)(29,31)(35,45,44,43)(41,42);(14,16)(15,21)(17,26)(18,27)(19,25)(20,32)(22,35)(23,34)(24,36)(28,39)(29,41)(30,40)(31,42)(33,43)(37,45)(38,44);(16,25)(21,34)(26,39)(27,40)(32,36)(35,44)(41,42)(43,45)1066 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26317);